/* Copyright (c) 2017-2020 Hans-Kristian Arntzen
 *
 * Permission is hereby granted, free of charge, to any person obtaining
 * a copy of this software and associated documentation files (the
 * "Software"), to deal in the Software without restriction, including
 * without limitation the rights to use, copy, modify, merge, publish,
 * distribute, sublicense, and/or sell copies of the Software, and to
 * permit persons to whom the Software is furnished to do so, subject to
 * the following conditions:
 *
 * The above copyright notice and this permission notice shall be
 * included in all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
 * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
 * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
 * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
 * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 */

#include "interpolation.hpp"

namespace Granite
{
float catmull_rom_spline(float c0, float c1, float c2, float c3, float phase)
{
	float phase2 = phase * phase;
	float phase3 = phase2 * phase;
	return c1 +
	       (c2 - c0) * 0.5f * phase +
	       (c0 - (2.5f * c1) + (2.0f * c2) - (0.5f * c3)) * phase2 +
	       ((-0.5f * c0) + (1.5f * c1) - (1.5f * c2) + (0.5f * c3)) * phase3;
}

// Computes the analytic derivative of the spline dFd(phase).
float catmull_rom_spline_gradient(float c0, float c1, float c2, float c3, float phase)
{
	float phase2 = phase * phase;
	return (c2 - c0) * 0.5f +
	       (c0 - (2.5f * c1) + (2.0f * c2) - (0.5f * c3)) * 2.0f * phase +
	       ((-0.5f * c0) + (1.5f * c1) - (1.5f * c2) + (0.5f * c3)) * 3.0f * phase2;
}
}